The Cosine–Sine Decomposition and Conditional Negative Correlation Inequalities for Determinantal Processes

André Goldman ()
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André Goldman: Institut Camille Jordan UMR 5208

Journal of Theoretical Probability, 2025, vol. 38, issue 1, 1-37

Abstract: Abstract For a conditional process of the form $$(\phi \vert A_{i} \not \subset \phi )$$ ( ϕ | A i ⊄ ϕ ) where $$\phi $$ ϕ is a basic elementary determinantal process, we obtain new negative correlation inequalities. Our approach relies upon the underlying geometric structure of the elementary discrete determinantal processes by using the canonical representation of a pair of subspaces in terms of principal vectors and angles, as well as the classical cosine–sine decomposition.

Keywords: Negative dependence; Spanning trees; BK (van den Berg–Kesten) inequality; Exterior algebra; Compound matrices; Jordan’s angles; 60K99; 60G55; 15A23; 68U99; 15A75 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10959-024-01393-7

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